$A$ uniformly charged half-ring of radius $R$ has a linear charge density $\sigma$. The electric potential at the centre of the half-ring is ($\epsilon_0$ = permittivity of free space).

Two identical thin rings,each of radius $R \text{ m}$,are coaxially placed at a distance $R \text{ m}$ apart. If $Q_1$ and $Q_2$ coulombs are the charges uniformly spread on the two rings respectively,the work done in moving a charge $q$ from the centre of one ring to that of the other is

If four charges $q_1 = +1 \times 10^{-8} \text{ C}$, $q_2 = -2 \times 10^{-8} \text{ C}$, $q_3 = +3 \times 10^{-8} \text{ C}$, and $q_4 = +2 \times 10^{-8} \text{ C}$ are kept at the four corners of a square of side $1 \text{ m}$, then the electric potential at the centre of the square is: (in $\text{ V}$)

Two point charges of $1 \text{ nC}$ and $2 \text{ nC}$ are placed at two corners of an equilateral triangle of side $3 \text{ cm}$. The work done in bringing a charge of $3 \text{ nC}$ from infinity to the third corner of the triangle is . . . . . . $\mu\text{J}$. $( \frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9} \text{ N.m}^{2}/\text{C}^{2} )$

$A$ spherical shell of radius $R$ carries a charge $Q$. What is the potential at point $B$ on the surface,at the center $A$,and at point $C$ at a distance $R/2$ from the center?

The electric potential on the surface of a charged spherical conductor of radius $5 \,cm$ is $200 \,V$. The work done in moving a charge of $+5 \,C$ from a point $A$ to another point $B$ situated at distances of $15 \,cm$ and $10 \,cm$ respectively from the centre of the sphere is (in $\,J$)